If you're comparing the 560ti and the HD6950, I have to vote for the 6950. I'm not 100% sure on power requirements for the 560ti, but I can tell you that the 6950 is a very heat-friendly and power-friendly card for the overall graphics power you get.
You'll probably be happy with both, but price-to-performance, I think the HD6950 represents one of the greatest values in GPU's right now. You can buy 1GB models for as low as $199 after mail in rebate. Plus, if you want to leave room for adding a second card later, the 6950's have shown to be tremendous cards when used in Crossfire. Either way you go, let me also put in a vote for the MSI Twin Frozr series - outstanding cooling and very quiet - excellent cards!